Alfeld, P., and D. Eyre, The exact analysis of sparse rectangular linear systems, ACM TOMS 17 (1991), 502--518. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Dimension and Local Bases of Homogeneous Spline Spaces - Alfeld, Neamtu, Schumaker (1995) (5 citations) (Correct)
....domain points has cardinality (7) #(G) V (d Gamma 1)E d Gamma 1 2 N: The importance of the HBB form of homogeneous polynomials is that it provides a simple way to describe when two such polynomials defined on adjoining trihedra join together smoothly. Indeed, suppose T [1] and T [2] are two trihedra generated by the sets fv1 ; v2 ; v3g and fv1 ; v3 ; v4g, respectively. Then as shown in [4] the two associated homogeneous polynomials p [1] and p [2] of degree d agree on the face shared by T [1] and T [2] in value and all derivatives up to order r if and only if (8) ....
....to describe when two such polynomials defined on adjoining trihedra join together smoothly. Indeed, suppose T [1] and T [2] are two trihedra generated by the sets fv1 ; v2 ; v3g and fv1 ; v3 ; v4g, respectively. Then as shown in [4] the two associated homogeneous polynomials p [1] and p [2] of degree d agree on the face shared by T [1] and T [2] in value and all derivatives up to order r if and only if (8) c [2] ijk = X =k c [1] i ; j B k (v4 ) for all k r; i j k = d; where B k are the Bernstein basis polynomials of degree k associated with T [1] By ....
[Article contains additional citation context not shown here]
P. Alfeld and D. Eyre,The exact analysis of sparse rectangular linear systems, ACM TOMS, 17 (1991), pp. 502--518.
Dimension and Local Bases of Homogeneous Spline Spaces - Peter Alfeld, Marian.. (5 citations) Self-citation (Alfeld) (Correct)
....points has cardinality #(G) V (d Gamma 1)E d Gamma 1 2 N: 2:5) The importance of the HBB form of homogeneous polynomials is that it provides a simple way to describe when two such polynomials defined on adjoining trihedra join together smoothly. Indeed, suppose T [1] and T [2] are two trihedra generated by the sets fv 1 ; v 2 ; v 3 g and fv 1 ; v 3 ; v 4 g, respectively. Then as shown in [4] the two associated homogeneous polynomials p [1] and p [2] of degree d agree on the face shared by T [1] and T [2] in value and all derivatives up to order r if and only ....
....when two such polynomials defined on adjoining trihedra join together smoothly. Indeed, suppose T [1] and T [2] are two trihedra generated by the sets fv 1 ; v 2 ; v 3 g and fv 1 ; v 3 ; v 4 g, respectively. Then as shown in [4] the two associated homogeneous polynomials p [1] and p [2] of degree d agree on the face shared by T [1] and T [2] in value and all derivatives up to order r if and only if c [2] ijk = X =k c [1] i ; j B k (v 4 ) for all k r; i j k = d; 2:6) where B k are the Bernstein basis polynomials of degree k associated with T [1] ....
[Article contains additional citation context not shown here]
Alfeld, P., and D. Eyre, The exact analysis of sparse rectangular linear systems, ACM TOMS 17 (1991), 502--518.
Bibliography on the Solution of Sparse Linear Systems and Related .. - Arantes (1997) (Correct)
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Alfeld, P. and Eyre, D. J. The exact analysis of sparse rectangular linear systems. ACM Trans. Math. Software, 17(4):502--518, 1991.
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